Question: $(-21+65i)+(-30+12i)=$ Express your answer in the form $(a+bi)$.
Explanation: Background Complex numbers can be added or subtracted by separately adding or subtracting their real and imaginary terms. To add or subtract complex numbers: Expand parentheses (attending to minus signs outside of parentheses if necessary) Combine all real terms (terms that do not contain $i$ ), and add or subtract them. Combine all imaginary terms (terms that contain $i$ ), and add or subtract them. Combining Like Terms $\begin{aligned} ({-21}+{65}i)+({-30}+{12}i)&={-21}+{65}i{-30}+{12}i \\\\ &={-21}{-30}+{65}i+{12}i \\\\ &={-51}+{77}i \end{aligned}$ Summary $({-21}+{65}i)+({-30}+{12}i)={-51}+{77}i$